Question: $\dfrac{ -8h - 4i }{ 8 } = \dfrac{ -5h - j }{ -2 }$ Solve for $h$.
Answer: Multiply both sides by the left denominator. $\dfrac{ -8h - 4i }{ {8} } = \dfrac{ -5h - j }{ -2 }$ ${8} \cdot \dfrac{ -8h - 4i }{ {8} } = {8} \cdot \dfrac{ -5h - j }{ -2 }$ $-8h - 4i = {8} \cdot \dfrac { -5h - j }{ -2 }$ Reduce the right side. $-8h - 4i = {8} \cdot \dfrac{ -5h - j }{ -{2} }$ $-8h - 4i = -{4} \cdot \left( -5h - j \right)$ Distribute the right side $-8h - 4i = -{4} \cdot \left( -{5h} - {j} \right)$ $-8h - 4i = {20}h + {4}j$ Combine $h$ terms on the left. $-{8h} - 4i = {20h} + 4j$ $-{28h} - 4i = 4j$ Move the $i$ term to the right. $-28h - {4i} = 4j$ $-28h = 4j + {4i}$ Isolate $h$ by dividing both sides by its coefficient. $-{28}h = 4j + 4i$ $h = \dfrac{ 4j + 4i }{ -{28} }$ All of these terms are divisible by $4$ Divide by the common factor and swap signs so the denominator isn't negative. $h = \dfrac{ -{1}j - {1}i }{ {7} }$